Thursday, 23 August 2012

Is there a word for "mathematics" in English? (part ii)

The more I read Bill Barton's book, The Language of Mathematics: telling mathematical tales, the more I become dismayed. I mean, I think there are excellent points in the book, but he treats everything so cursory that the points he make are never really carried to their logical conclusions. He says that he has no linguistic expertise but he's not really a maths expert either (confuses maths for arithmetic in many spots).

But what really concerns me is that what he calls "evidence" is not really discussed in dialectic terms but are rather more selective than that (many times he says that "evidence" supports his thesis, though what that is he never really makes explicit). I'm pretty sure that Barton is an excellent teacher, a decent human being, and utterly well-meaning. But his goal seems to be a foregone conclusion: English good; aboriginal languages not so good:

...if mathematics arises from language, then we must consider mathematics in the same way we consider language. Different concepts are expressed in different languages, and some concepts are extremely difficult, some say impossible, to translate between languages. The implication is that different quantitative, relational, and spatial concepts may also not be easily transformed into each other. The language investigations reported in Part I confirm this. [emphasis added by me] (p. 69)

I would suggest that English itself is relatively "inferior" as a vehicle for mathematics discourse as compared to French (a descendent of Latin) and German (which has the capacity to agglutinate grammatical/lexical elements together to construct new concepts all in German), demonstrably contrary to Barton's statement that English is "naturally" adaptable to mathematical speak (based solely upon notion that English can change the grammatical function of number from adjective to noun - so can every other language, the polysynthetic Inuktitut being an epitome of that wonderful adaptability: a verb can be changed into a noun, and vice-versa):

Sometimes numbers are used in their adjectival sense and in their nominal sense in the same sentence. "Three fives are fifteen." The three is adjectival, the five and fifteen are nominal - the five is even made into a plural (there are three of them, just like you can have three hugs or three kisses). The important point is that all of this feels[emphasis added by me] quite natural in English, we are not even aware of the different grammatical uses of number words, and we move between them quite easily depending on what we are trying to say.This is not the case with all languages. (p. 42)

Barton mentions Wittenstein (one of the thinkers I myself consider great) but fails to mention that Wittenstein treated language and mathematics in Formalist terms in his Philosophische Untersuchungen (Philosophical Investigations, 1953). Barton doesn't take anything from Wittenstein, really: the grammatical rules of language and maths are, at their cores, just formal rules (Wittenstein says) but it is the social uses of them that imbue "meaning" upon the human act of "communication". Take care not to forget this (says Wittenstein in not so many words) lest language is used against you.

I think Barton suffers from covert (or subconscious, or unexamined) Anglophilism. Like many others living in a colonialist countries, he seems to suffer from unvoiced historical "guilt" of subsuming a whole group of people so he's making half-hearted attempts at justifying the whys and wherefores English is the language of modernity rather than focussing on what each language has to offer to the discourse.

I say: get over it. You have so much to offer; there is also no shame in learning from other languages. Re-read your Wittenstein, your John Dewey, your Vygotsky... English is no more privileged than any other language. You owe the Maori your whole being as a teacher: nothing less is social justice.

Epistemological cross-pollination is what makes human intelligence/knowledge/potential so rich and diverse (but there's always room for improvement). This should be an axiom in cross-cultural relations. The other axiom should be that human knowledge and intelligence is not language-specific, and is, at its core, completely democratic. It takes talent to bring that out; talent can be cultivated.